Fractional supersymmetry and hierarchy of shape invariant potentials

Details Fractional supersymmetry and hierarchy of shape invariant potentials Fractional supersymmetry and hierarchy of shape invariant potentials

2006-09-04

arxiv.org/abs/quant-ph/0609017v3

J.Math.Phys.47:122108,2006

Physics

Quantum Physics

15 pages; version 2: introduction and conclusion enlarged, acknowledgment added, references added; version 3: one reference ad

Scientific paper

10.1063/1.2401711

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra. The Hamiltonian gives rise to a hierarchy of isospectral Hamiltonians. Special cases of the algebra lead to dynamical systems for which the isospectral supersymmetric partner Hamiltonians are connected by a (translational or cyclic) shape invariance condition.

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